Preframe presentations present

  • Peter Johnstone
  • Steven Vickers
Part I
Part of the Lecture Notes in Mathematics book series (LNM, volume 1488)

Abstract

Preframes (directed complete posets with finite meets that distribute over the directed joins) are the algebras for an infinitary essentially algebraic theory, and can be presented by generators and relations. This result is combined with a general argument concerning categories of commutative monoids to give a very short proof of the localic Tychonoff Theorem.

It is also shown how frames can be presented as preframes, a result analogous to Johnstone's construction of frames from sites, and an application is given.

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Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • Peter Johnstone
    • 1
  • Steven Vickers
    • 2
  1. 1.Department of Pure Mathematics and Mathematical StatisticsUniversity of CambridgeCambridge
  2. 2.Department of ComputingImperial CollegeLondon

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